Suppose that 6 economists who work for the federal government and 7 university economists were asked to grade the effectiveness of the federal government's stimulus bill in terms of its ability to increase jobs over the next two years. The grades are shown below. Do the two groups differ in terms of their opinion?
a. What nonparametric method is appropriate for analyzing these data?
b. Are the assumptions satisfied for applying this method? Explain.
c. State the null and alternative hypotheses.
d. Perform the test and state your conclusion at α = 0.10.

Question

Suppose that 6 economists who work for the federal government and 7 university economists were asked to grade the effectiveness of the federal government's stimulus bill in terms of its ability to increase jobs over the next two years. The grades are shown below. Do the two groups differ in terms of their opinion?
  a. What nonparametric method is appropriate for analyzing these data?
b. Are the assumptions satisfied for applying this method? Explain.
c. State the null and alternative hypotheses.
d. Perform the test and state your conclusion at α = 0.10.

Quizplus · Accepted Answer

The Answer is a. Wilcoxon rank-sum / Mann-Whitney test.
b. Yes. We can assume that the sampled observations are independent (Independence Assumption) and the two groups are independent of each other (Independent Groups Assumption).
c. H0: The government and university economists have the same typical opinion.
HA: The government and university economists have different typical opinions.
d.

a. Wilcoxon rank-sum / Mann-Whitney test. b. Yes. We can assume that the sampled observations are independent (Independence Assumption) and the two groups are independent of each other (Independent Groups Assumption). c. H0: The government and university economists have the same typical opinion. HA: The government and university economists have different typical opinions. d. The ranks in the table above order all the opinions from the worst (Cs assigned rank1.5) to the best (A assigned rank 13). We get T1 = TGovernment = 55.5 and T2 = TUniversity = 35.5. The test statistic is T = min (55.5 , 35.5) = 35.5. The critical values from the table W1 are TL = 30 and TU = 54. Therefore, we fail to reject the null hypothesis. At α = 0.10, there is no evidence that the government and university economists have different typical opinions about the economic stimulus bill.

The ranks in the table above order all the opinions from the worst (Cs assigned rank1.5) to the best (A assigned rank 13). We get T1 = TGovernment = 55.5 and T2 = TUniversity = 35.5. The test statistic is T = min (55.5 , 35.5) = 35.5. The critical values from the table W1 are TL = 30 and
TU = 54. Therefore, we fail to reject the null hypothesis. At α = 0.10, there is no evidence that the government and university economists have different typical opinions about the economic stimulus bill.

Suppose That 6 Economists Who Work for the Federal Government